This study presents a tri-layer broadband metamaterial absorber which operates in the GHz range. The absorber was composed of a polyhedral iron-cobalt alloy/graphite nanosheet material arranged in a flat sheet with two punched-in rings for the top layer, a continuous FR-4 layer at the middle, and a continuous copper layer at the bottom. For the normal incidence of electromagnetic wave, the proposed absorber demonstrated an exceptional broadband absorption in a frequency range of 7.9-14.6 GHz, revealing an absorption exceeding 90%. The absorption magnitude remains to be above 90% in a frequency range of 8-11.1 GHz for transverse-electric-polarized waves at incident angles up to 55°. For both transverse-magnetic- and electric-polarized waves, the absorption exceeds 90% in a frequency range of 9.5-14.6 GHz. The physical mechanism behind the absorption properties is analyzed thoroughly through the electric- and magnetic-field distributions. The obtained results could contribute potentially to the development of microwave applications based on metamaterial absorbers, such as radar-stealth technology, electromagnetic shielding for health safety and reduced electromagnetic interferences for high-performance communications and electronic devices.